Question: The grades on a language midterm at Almond are normally distributed with $\mu = 75$ and $\sigma = 5.5$. Michael earned a n $84$ on the exam. Find the z-score for Michael's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Michael's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{84 - {75}}{{5.5}}} $ ${ z \approx 1.64}$ The z-score is $1.64$. In other words, Michael's score was $1.64$ standard deviations above the mean.